Tuning fork gyroscope time domain inertial sensor

FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT

This invention is assigned to the United States Government and is available for licensing for commercial purposes. Licensing and technical inquiries may be directed to the Office of Research and Technical Applications, Space and Naval Warfare Systems Center, Pacific, Code 7274, San Diego, Calif., 92152; voice (619) 553-572; ssc_pac_t2@navy.mil. Reference Navy Case Number 101330.

BACKGROUND OF THE INVENTION

The invention disclosed herein relates to the field of gyroscopic inertial sensing. Highly stable and accurate micro-electrical-mechanical system (MEMS) gyroscopes are needed for navigational inertial sensing. Larger gyroscopes can meet the accuracy requirements needed for inertial navigation, but are expensive and require more space than a MEMS gyroscope. Current MEMS gyroscopes are subject to electronic and mechanical noise, non-linearity, and drift in mechanical parameters which cause error to their measurements. Conventional MEMS tuning fork gyroscopes use capacitance to measure the offset caused by the Coriolis force. A need exists for a more accurate and more stable tuning fork gyroscope.

SUMMARY

Disclosed herein is an inertial-sensing-capable tuning fork gyroscope comprising a frame, a tuning fork, and at least two digital position triggers. The tuning fork comprises a base and first and second prongs. The base has proximal and distal ends. The proximal end is coupled to the frame and the distal end is coupled to the first and second prongs. The first and second prongs are driven by first and second drivers respectively to oscillate with respect to the frame in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The digital position triggers are operatively coupled to the frame and to the tuning fork. Each position trigger is configured to experience at least two trigger events during each oscillation of the tuning fork in a second direction. The second direction is orthogonal to the first direction.

The tuning fork gyroscope disclosed herein may be used for inertial sensing according to the method. The first step provides for driving first and second prongs of the tuning fork gyroscope to oscillate with respect to a frame of the tuning fork gyroscope in a first direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The second step provides for monitoring closed and open states of two pairs of second-direction-stacked electron-tunneling-tip switches, wherein the second direction is orthogonal to the first direction, and wherein each pair of switches is operatively coupled to the frame and the tuning fork such that each pair of switches passes through at least two closed states during each oscillation of the tuning fork in the second direction. The third step provides for measuring the time interval between closed states of each switch pair to characterize the offset of the tuning fork in the second direction. The fourth step provides for determining the Coriolis forces acting on the tuning fork gyroscope by calculating the offset of the tuning fork in the second direction.

An alternative embodiment of the tuning fork gyroscope comprises a frame, a tuning fork, first and second drivers, and first and second pairs of electron-tunneling tip switches. The tuning fork comprises a base and first and second prongs, wherein a proximal end of the base is coupled to the frame and wherein proximal ends of the first and second prongs are coupled to a distal end of the base. The first driver is operatively coupled to the first prong such that the first driver is configured to drive the first prong to oscillate with respect to the frame in a first direction at the first prong's resonant frequency. The second driver is operatively coupled to the second prong such that the second driver is configured to drive the second prong to oscillate with respect to the frame in the first direction at the second prong's resonant frequency and 180° out of phase with the first prong. The first pair of electron-tunneling tip switches is operatively coupled to the frame and a first location on the tuning fork such that the first pair of switches is configured to switch from an open state to a closed state at least twice during a complete oscillation of the tuning fork with respect to the frame in the second direction. The second pair of electron-tunneling tip switches is operatively coupled to the frame and to a second location on the tuning fork such that the second pair of switches is configured to switch from an open state to a closed state at least twice during a complete oscillation of the tuning fork with respect to the frame in the second direction.

BRIEF DESCRIPTION OF THE DRAWINGS

Throughout the several views, like elements are referenced using like references. The elements in the figures are not drawn to scale and some dimensions are exaggerated for clarity.

<figref idref="DRAWINGS">FIG. 1</figref> is a top view illustration of an embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIGS. 2A-2B</figref> represent a perspective view of an example MEMS embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIG. 3A</figref> is a partial perspective view of the MEMS embodiment of the gyroscope depicted in <figref idref="DRAWINGS">FIGS. 2A and 2B</figref>.

<figref idref="DRAWINGS">FIG. 3B</figref> is a side view of an embodiment of a digital trigger.

<figref idref="DRAWINGS">FIGS. 4A-4C</figref> illustrate side views of various reference positions of the digital trigger shown in <figref idref="DRAWINGS">FIG. 3B</figref>.

<figref idref="DRAWINGS">FIG. 5</figref> is a flowchart illustrating one example of how the gyroscope depicted in <figref idref="DRAWINGS">FIGS. 2A-3B</figref> may be used for time-domain inertial sensing.

<figref idref="DRAWINGS">FIG. 6</figref> is a plot of the displacement of a tuning fork with respect to a frame.

<figref idref="DRAWINGS">FIG. 7</figref> is a plot of tuning fork displacement against time in the presence of external forcing.

<figref idref="DRAWINGS">FIG. 8A</figref> is a plot of the oscillation amplitude of a tuning fork with respect to a frame.

<figref idref="DRAWINGS">FIG. 8B</figref> is, in part, a pictorial representation of triggering events.

<figref idref="DRAWINGS">FIG. 9</figref> is a top view of an embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIG. 10</figref> is a side cross-section side view of an embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIG. 11</figref> is a plot of the displacement of conductive tips over time with respect to a conductive plane.

<figref idref="DRAWINGS">FIG. 12</figref> is a graph showing the displacement of conductive tips.

<figref idref="DRAWINGS">FIG. 13</figref> is another plot of the displacement of conductive tips over time with respect to a conductive plane.

<figref idref="DRAWINGS">FIG. 14</figref> is another graph showing the displacement of conductive tips.

<figref idref="DRAWINGS">FIGS. 15A-15B</figref> are perspective views of an embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIG. 16</figref> is a perspective view of an embodiment of a tuning fork gyroscope.

<figref idref="DRAWINGS">FIG. 17</figref> is a perspective view of another embodiment of a tuning fork gyroscope.

DETAILED DESCRIPTION OF EMBODIMENTS

<figref idref="DRAWINGS">FIG. 1</figref> is a top view illustration of a tuning fork gyroscope <b>10</b> capable of time-domain inertial sensing. The gyroscope <b>10</b> comprises a frame <b>12</b>, a tuning fork <b>14</b>, first and second drivers <b>16</b> and <b>18</b> respectively, and at least two digital position triggers <b>20</b>. The tuning fork <b>14</b> comprises a base <b>22</b> and first and second prongs <b>24</b> and <b>26</b> respectively. The base <b>22</b> has a proximal end <b>28</b> and a distal end <b>30</b>. The base's proximal end <b>28</b> is coupled to the frame <b>12</b> and the distal end <b>30</b> is coupled to the first and second prongs <b>24</b> and <b>26</b>. The first and second drivers <b>16</b> and <b>18</b> are configured to drive the first and second prongs <b>24</b> and <b>26</b> respectively to oscillate with respect to the frame <b>12</b> in a first direction such that the prongs <b>24</b> and <b>26</b> oscillate at their respective resonant frequencies and 180° out of phase with each other. In <figref idref="DRAWINGS">FIG. 1</figref>, the first direction corresponds to the x-direction. However, it is to be understood that the first and second prongs <b>24</b> and <b>26</b> may be driven to oscillate in any desired direction and the x-direction is only offered as one example. The digital position triggers <b>20</b> are operatively coupled to the frame <b>12</b> and to the tuning fork <b>14</b>. Each position trigger <b>20</b> is configured to experience at least two trigger events during each oscillation of the tuning fork <b>14</b> in a second direction, which is orthogonal to the first direction. In <figref idref="DRAWINGS">FIG. 1</figref>, the second direction corresponds to the z-direction.

The gyroscope <b>10</b> may be manufactured on any scale. For example, in one embodiment the gyroscope <b>10</b> may be monolithically integrated into a micro-electro-mechanical system (MEMS) device. The gyroscope <b>10</b> may be used in any orientation. Although the x-y-z coordinate system is depicted in the drawings and referred to herein, it is to be understood that the first, second, and third directions/axes, as used herein, may correspond to any three mutually-orthogonal directions/axes in any three-dimensional coordinate system.

The frame <b>12</b> may be any size and shape, and be made of any material capable of providing rigid support for the gyroscope <b>10</b> such that the frame <b>12</b> does not significantly flex and/or deform when exposed to lateral and rotational accelerations of the gyroscope <b>10</b>.

The first and second drivers <b>16</b> and <b>18</b> may each be any apparatus capable of causing the first and second prongs <b>24</b> and <b>26</b> to oscillate at any desired frequency in the x-direction with respect to the frame <b>12</b>. Suitable examples of the first and second drivers <b>16</b> and <b>18</b> include, but are not limited to, variable area actuators, such as electrostatic comb drives (such as are portrayed in <figref idref="DRAWINGS">FIG. 2B</figref>), variable gap actuators, such as parallel plate actuators, and other electro-magnetic or piezoelectric mechanisms of actuation. Each of the first and second prongs <b>24</b> and <b>26</b> may be driven using a continuous oscillating force or by periodic “delta function” forces in phase with the given prong's harmonic resonance.

The digital trigger <b>20</b> may be any apparatus capable of producing digital signals corresponding to various positions of a section of the tuning fork (i.e., the section to which the given digital trigger <b>20</b> is attached) with respect to the frame <b>12</b>. For example, the digital trigger <b>20</b> may be any device capable of experiencing a change in state based on positional changes of the tuning fork <b>14</b> relative to the frame <b>12</b>. Other examples of the digital trigger <b>20</b> include an electron tunneling switch, a capacitive switch, an optical shutter switch, and a magnetic switch. A purpose of the digital trigger <b>20</b> is to localize the position of the section to which the given digital trigger <b>20</b> is attached and the frame <b>12</b> such that an accurate acceleration-independent phase measurement can be performed—thereby increasing stability of a phased-locked loop closure and reducing overall phase noise and jitter of the gyroscope <b>10</b>.

<figref idref="DRAWINGS">FIGS. 2A-2B</figref> represent a perspective view of an example MEMS embodiment of the gyroscope <b>10</b>. In the embodiment shown, the first and second drivers <b>16</b> and <b>18</b> are capacitive comb drives, and the digital triggers <b>20</b> are stacked pairs of electron tunneling switches (only the top switch is visible in <figref idref="DRAWINGS">FIG. 2B</figref>) capable of generating a finite width current pulse which “tunnels from conductive tips <b>32</b> on the first and second prongs <b>24</b> and <b>26</b> to a conductive plane <b>34</b> on the frame <b>12</b>.

<figref idref="DRAWINGS">FIG. 3A</figref> is a partial perspective view of the MEMS embodiment of the gyroscope <b>10</b> depicted in <figref idref="DRAWINGS">FIGS. 2A and 2B</figref>. <figref idref="DRAWINGS">FIG. 3A</figref> shows the orientation of the first prong <b>24</b> with respect to the frame <b>12</b>. In this embodiment a conductive layer <b>36</b> and an optional lower conductive layer <b>38</b> are also depicted. <figref idref="DRAWINGS">FIG. 3B</figref> is a side view of one embodiment of a digital trigger <b>20</b> such as may be used in the example embodiment of the gyroscope <b>10</b> depicted in <figref idref="DRAWINGS">FIGS. 2A</figref>, <b>2</b>B, and <b>3</b>A. In this embodiment, the digital trigger <b>20</b> comprises a pair of electron tunneling switches <b>40</b>. The pair of electron tunneling switches <b>40</b> comprises a stacked conductive tips <b>32</b>, and stacked conductive planes <b>34</b>. The tips <b>32</b> and the planes <b>34</b> are separated from each other in the y-direction by a gap <b>42</b>. The tips <b>32</b> and the planes <b>34</b> are separated from each other in the z-direction by a dielectric layer <b>44</b>.

<figref idref="DRAWINGS">FIGS. 4A-4C</figref> illustrate an embodiment of the digital trigger <b>20</b> shown in <figref idref="DRAWINGS">FIG. 3B</figref> where the pair of electron tunneling switches is configured to pass through multiple closed states corresponding to multiple reference positions of the first prong <b>24</b> with respect to the frame <b>12</b> during a single oscillation period. When the first prong <b>24</b> is in the first reference position with respect to the frame <b>12</b> the tunneling tips <b>32</b> are aligned with the conductive planes <b>34</b> and the digital trigger <b>20</b> is in a closed state such that a current pulse may pass from the tips <b>32</b> to the planes <b>34</b>, as depicted by the arrows. The electron tunneling tips <b>32</b> are aligned with each other in the z-direction and separated from each other in the z-direction by a distance d₁. The conductive planes <b>34</b> are also aligned with each other in the z-direction and separated from each other in the z-direction by the distance d₁.

When the first prong <b>24</b> is in the first reference position, or zero force position, such as is depicted in <figref idref="DRAWINGS">FIG. 4A</figref>, a current pulse passes from the each of the tunneling tips <b>32</b> over the gap <b>42</b> to a corresponding plane <b>34</b>. This embodiment of the digital trigger <b>20</b> also comprises second and third reference positions of the first prong <b>24</b> with respect to the frame <b>12</b>. The first prong <b>24</b> is in the second reference position when the first prong <b>24</b> is displaced from the first reference position in the z-direction by the distance +d₁, such as is shown in <figref idref="DRAWINGS">FIG. 4B</figref>. In the second reference position, the digital trigger <b>20</b> is in a closed state such that a current pulse may pass from the lower of the two tips <b>32</b> to the upper of the two planes <b>34</b>. The first prong <b>24</b> is in the third reference position when the first prong <b>24</b> is displaced in the z-direction by the distance −d₁, such as is shown in <figref idref="DRAWINGS">FIG. 4C</figref>. In the third reference position, the digital trigger <b>20</b> is in a closed state such that a current pulse passes from the upper of the two tips <b>32</b> to the lower of the two planes <b>34</b>.

<figref idref="DRAWINGS">FIG. 5</figref> is a flowchart illustrating one example of how the gyroscope <b>10</b> depicted in <figref idref="DRAWINGS">FIGS. 2A-3B</figref> may be used for time-domain inertial sensing. The first step <b>46</b> provides for driving the first and second prongs <b>24</b> and <b>26</b> of the tuning fork <b>14</b> to oscillate with respect to the frame <b>14</b> in the x-direction, such that the prongs oscillate at their respective resonant frequencies and 180° out of phase with each other. The second step <b>48</b> provides for monitoring the closed and open states of the two pairs of electron-tunneling-tip switches <b>40</b>. The third step <b>50</b> provides for measuring the time interval between closed states of each switch pair <b>40</b> to characterize the offset of the tuning fork <b>14</b> in the z-direction. The fourth step <b>52</b> provides for determining the Coriolis forces acting on the tuning fork gyroscope <b>10</b> by calculating the offset of the tuning fork <b>14</b> in the z-direction. The oscillation amplitude calculation of a given prong in the z-direction may be based on the time interval between successive closed states of the prong's switch pair <b>40</b>. The Coriolis force acting on a given prong may be expressed as a change in amplitude of the z-direction oscillation of the given prong when both the z-direction resonant frequency and the x-direction resonant frequency of the given prong match. The Coriolis force may be expressed as the z-direction offset of the resonant oscillation of the tuning fork <b>14</b> in the z-direction when the resonant frequency of a given prong in the z-direction is much greater than that of the prong's resonant frequency in the x-direction.

<figref idref="DRAWINGS">FIG. 6</figref> is a plot of the displacement of the tuning fork <b>14</b> with respect to the frame <b>12</b>. The exemplary time domain-based method represented in <figref idref="DRAWINGS">FIG. 5</figref> is in the context of sensing a force, and relies on measuring deflection (also referred to as the bias) of the tuning fork <b>14</b>, which may also be characterized as a proof mass/spring-based oscillator that is being driven at a frequency f_drv. In one configuration, the oscillations of the oscillator are substantially harmonic. Alternatively, the oscillations may be substantially non-harmonic or (e.g., not perfect sinusoids).

As a brief aside, in classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F that is proportional to the displacement x as: <br /><i>F=−kx.</i>  (Eqn. 1)

If the restoring force is the only force acting on the oscillator system, the system is referred to as a simple harmonic oscillator, and it undergoes simple harmonic motion, characterized by sinusoidal oscillations about the equilibrium point, with constant amplitude and constant frequency f₀(which does not depend on the amplitude):

<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mrow><mfrac><mn>1</mn><msub><mi>T</mi><mn>0</mn></msub></mfrac><mo>=</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi></mrow></mfrac><mo>⁢</mo><mrow><msqrt><mfrac><mi>k</mi><mi>m</mi></mfrac></msqrt><mo>.</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mi>Eqn</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>⁢</mo><mn>2</mn></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><img file="US8991250B2_D0001.tif" /><br /> where: <ul id="ul0001" list-style="none"><li id="ul0001-0001" num="0000"><ul id="ul0002" list-style="none"><li id="ul0002-0001" num="0040">k is the spring constant;</li><li id="ul0002-0002" num="0041">m is the oscillator mass</li><li id="ul0002-0003" num="0042">f₀is the oscillator resonant frequency; and</li><li id="ul0002-0004" num="0043">T₀is the corresponding period of oscillations.</li></ul></li></ul>

In the plot shown in <figref idref="DRAWINGS">FIG. 6</figref> (“harmonic” variant), the driving frequency f_drvis configured to match the natural resonance frequency f₀of the proof mass/spring-based harmonic oscillator causing a sinusoidal motion of the proof mass, as shown by the trace <b>54</b>. A system driven in-resonance typically requires a high-quality factor (Q) oscillating proof-mass system. It will be appreciated, however, that for this embodiment, literally any driving signal that maintains the oscillator in resonance may be used.

In another example embodiment (not shown), the proof mass of the oscillator may be driven “off-resonance”, which provides, inter alia, precise control of the oscillation period and, hence, control of sensor accuracy. Off-resonance driven systems typically require a lower Q oscillator.

In the absence of any external forcing, the proof mass trajectory is centered at a reference position <b>56</b>, as shown in <figref idref="DRAWINGS">FIG. 6</figref>. The oscillatory motion of the proof mass is measured using “triggering” events that are generated when the mass passes through trigger points corresponding to predefined physical locations such as the first, second, and third reference positions depicted in <figref idref="DRAWINGS">FIGS. 4A-4C</figref>. The first reference position corresponds to a neutral (also referred to as a zero-force) point <b>56</b>. The second reference position corresponds to a positive trigger point <b>58</b>. The third reference position corresponds to a negative trigger point <b>60</b>. In the plot of <figref idref="DRAWINGS">FIG. 6</figref>, the trigger positions <b>58</b> and <b>60</b> are configured at the same predetermined distance d₀<b>62</b> (also referred to as the trigger gap or trigger spacing) away from the first reference position <b>56</b>. As will be appreciated by those skilled in the art, other trigger configurations are compatible with the invention, such as, for example, asymmetric and/or multiple sets of positive and or negative trigger points <b>58</b>, <b>60</b>. In one specific variant, a single trigger position (such as the first reference position <b>56</b> for example) is utilized.

In the plot of <figref idref="DRAWINGS">FIG. 6</figref>, the harmonic oscillations of the tuning fork/proof mass (as shown for example by the un-forced trace <b>54</b>) causes each of the triggering points <b>56</b>, <b>58</b>,<b>60</b> to generate a pair of triggering events marked by the circles <b>64</b>, triangles <b>66</b>, and squares <b>68</b>, respectively, for each full cycle of mass oscillation.

Timing of the triggering events <b>64</b>, <b>66</b>, <b>68</b> is measured using the same reference clock, and periods between successive crossings of the respective trigger points are computed. That is, the period Tr₁(denoted by the reference character <b>70</b>) is determined by subtracting the times of the successive trigger events <b>64</b> (which correspond to the mass crossing of the reference trigger point <b>56</b>). The period Tr₂(denoted by the reference character <b>72</b>) is determined by subtracting the times of the successive trigger events <b>66</b> (which correspond to the mass crossing of the positive trigger point <b>58</b>). The period Tr₃(denoted by the reference character <b>74</b>) is determined by subtracting the times of the successive trigger events <b>68</b> (which correspond to the mass crossing of the reference point <b>60</b>).

When the proof mass is subjected to an external force F_extof a frequency f_ext&lt;f_drv, the equilibrium point of the proof mass harmonic oscillations is shifted from the reference zero-force position. That is, a low frequency forces acting on the proof mass results in a low frequency shift (also referred to as the deflection) of the equilibrium point. Because applied inertial forces impact the DC bias of the simple harmonic oscillator, it is by definition immune to other zero-mean frequencies that may be coupled into the harmonic oscillator; that is, any high frequency oscillation centered around mean value (e.g., zero) will average to that mean value.

<figref idref="DRAWINGS">FIG. 7</figref> is a plot of tuning fork displacement against time in the presence of external forcing. As indicated by the trace <b>76</b> the oscillations of the proof mass in the presence of external forcing are shifted from the zero-force oscillations trajectory. As a result, the forced oscillation trace <b>76</b> is centered around a level (indicated by the line <b>78</b>) that is deflected from the reference point <b>56</b>.

Similar to the mass motion described with respect to <figref idref="DRAWINGS">FIG. 6</figref>, harmonic oscillations of the proof mass in the presence of external forcing (e.g., the trace <b>76</b> in <figref idref="DRAWINGS">FIG. 7</figref>) cause each of the triggering points <b>56</b>, <b>58</b>, and <b>60</b> to generate a pair of triggering events marked by circles <b>80</b>, triangles <b>82</b>, and squares <b>84</b>, respectively, for each full cycle of mass oscillation. The external force acts to create an offset (bias) in the oscillator, which is detected by measuring the time periods between successive triggering points (such as the points <b>80</b>, <b>82</b>, and <b>84</b> in <figref idref="DRAWINGS">FIG. 7</figref>), as described in detail below.

Measured timing of the triggering events <b>80</b> is used to compute the period T₁(denoted by the arrow <b>86</b>), which corresponds to the forced mass crossing of the reference trigger point <b>56</b> on the upswing of the mass oscillation. The period T₂(denoted by the arrow <b>88</b>) is determined by subtracting the times of the successive trigger events <b>82</b>, and T<b>2</b> corresponds to the mass crossing of the positive trigger point <b>58</b>. The period T₃(denoted by the arrow <b>90</b>) is determined by subtracting the times of the successive trigger events <b>84</b>, and it corresponds to the mass crossing of the reference point <b>60</b>. The period T₄(denoted by the arrow <b>92</b>) is determined by subtracting the times of the successive trigger events <b>80</b> and corresponds to the forced mass crossing of the reference trigger point <b>56</b> on the downswing of the mass oscillation, as illustrated in <figref idref="DRAWINGS">FIG. 7</figref>.

In one exemplary approach, the measured periods between successive trigger events (i.e., T₁through T₄) are used to obtain an estimate of the proof mass deflection d (denoted by the arrow <b>94</b> in <figref idref="DRAWINGS">FIG. 7</figref>) from the reference point. The proof mass deflection d₊ around the oscillation maximum (as depicted by the arrow <b>96</b> in <figref idref="DRAWINGS">FIG. 7</figref>) is obtained by combining the upswing reference point crossing period T₁and the positive trigger point <b>58</b> crossing period T₂as follows:

<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mi>d</mi><mo>+</mo></msub><mo>=</mo><mrow><msub><mi>A</mi><mo>+</mo></msub><mo>⁢</mo><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>1</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow><mo>,</mo><mrow><msub><mi>A</mi><mo>+</mo></msub><mo>=</mo><mfrac><msub><mi>d</mi><mn>0</mn></msub><mrow><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>2</mn></msub></mrow><mi>P</mi></mfrac></mrow><mo>-</mo><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>1</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow></mfrac></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mi>Eqn</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>⁢</mo><mn>3</mn></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><img file="US8991250B2_D0002.tif" /><br /> where: d₀is the distance between the reference trigger point and the positive trigger point (the trigger gap); <ul id="ul0003" list-style="none"><li id="ul0003-0001" num="0000"><ul id="ul0004" list-style="none"><li id="ul0004-0001" num="0055">A₊ is the amplitude of the oscillations at the oscillation maxima;</li><li id="ul0004-0002" num="0056">P is the period of oscillations defined as P=T₁+T₃;</li><li id="ul0004-0003" num="0057">d₊ is the proof mass deflection estimate around the oscillation maxima;</li><li id="ul0004-0004" num="0058">T₁is the upswing reference point crossing period; and</li><li id="ul0004-0005" num="0059">T₂is the positive trigger point crossing period. <br /> Similarly, the proof mass deflection d₋ around the oscillation minimum is (as depicted by the arrow <b>98</b> in <figref idref="DRAWINGS">FIG. 7</figref>) obtained by combining the upswing reference point crossing period T₃and the negative trigger point crossing period T₄as follows: </li></ul></li></ul>

<maths id="MATH-US-00003" num="00003"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mi>d</mi><mo>-</mo></msub><mo>=</mo><mrow><msub><mi>A</mi><mrow><mo>-</mo><mn>0</mn></mrow></msub><mo>⁢</mo><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>3</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow><mo>,</mo><mrow><msub><mi>A</mi><mo>-</mo></msub><mo>=</mo><mfrac><msub><mi>d</mi><mn>0</mn></msub><mrow><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>4</mn></msub></mrow><mi>P</mi></mfrac></mrow><mo>-</mo><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>3</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow></mfrac></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mi>Eqn</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>⁢</mo><mn>4</mn></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><img file="US8991250B2_D0003.tif" /><br /> where: d₀is the trigger gap; <ul id="ul0005" list-style="none"><li id="ul0005-0001" num="0000"><ul id="ul0006" list-style="none"><li id="ul0006-0001" num="0061">A_ is the amplitude of the oscillations at the oscillation minima;</li><li id="ul0006-0002" num="0062">P is the period of oscillations defined as P=T₁+T₃;</li><li id="ul0006-0003" num="0063">d₋ is the proof mass deflection estimate around the oscillation minima;</li><li id="ul0006-0004" num="0064">T₃is the downswing reference point crossing period; and</li><li id="ul0006-0005" num="0065">T₄is the negative trigger point crossing period.</li></ul></li></ul>

In one variant, two independent estimates, d₊ and d₋, are used to provide deflection measurements twice in each cycle (which may or may not be every half cycle) of oscillations, hence improving sensor frequency response. In another variant, the independent estimates d₊, d₋ are combined to produce an averaged deflection d thereby reducing measurement short term error. In yet another variant, an averaging window of variable length is used to further improve measurement precision.

In the deflection estimations according to Eqns. 3 and 4, the period of oscillation P is measured every oscillation cycle and the periods T₁through T₄are defined in <figref idref="DRAWINGS">FIG. 7</figref>. Note that the calculated deflection is independent of the amplitude of oscillation.

In one embodiment useful for acceleration force measurements, the accelerations corresponding to the deflection derived from the Eqns. 3 and 4 are obtained as follows:

<maths id="MATH-US-00004" num="00004"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mi>a</mi><mo>+</mo></msub><mo>=</mo><mrow><msup><mrow><msub><mi>d</mi><mn>0</mn></msub><mo>⁡</mo><mrow><mo>(</mo><mfrac><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi></mrow><mi>P</mi></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>⁢</mo><mfrac><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>1</mn></msub></mrow><mi>P</mi></mfrac></mrow><mrow><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>1</mn></msub></mrow><mi>P</mi></mfrac></mrow><mo>-</mo><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>2</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow></mfrac></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mi>Eqn</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>⁢</mo><mn>5</mn></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>a</mi><mo>-</mo></msub><mo>=</mo><mrow><msup><mrow><msub><mi>d</mi><mn>0</mn></msub><mo>⁡</mo><mrow><mo>(</mo><mfrac><mrow><mn>2</mn><mo>⁢</mo><mi>π</mi></mrow><mi>P</mi></mfrac><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>⁢</mo><mfrac><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>3</mn></msub></mrow><mi>P</mi></mfrac></mrow><mrow><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>4</mn></msub></mrow><mi>P</mi></mfrac></mrow><mo>-</mo><mrow><mi>cos</mi><mo>⁢</mo><mfrac><mrow><mi>π</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>T</mi><mn>3</mn></msub></mrow><mi>P</mi></mfrac></mrow></mrow></mfrac></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mi>Eqn</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>⁢</mo><mn>6</mn></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><img file="US8991250B2_D0004.tif" />

The derivation of Eqns. 3 and 4 assumes that the external force is constant throughout the measurements of T₁through T₄, which places a limit on the highest frequency of the external force that can be accurately resolved using these equations. Therefore, in the case of a continuous driving signal, it is necessary to select a driving frequency f_drvthat is higher than the maximum expected forcing frequency: i.e. f_ext&lt;f_drv.

As is seen from Eqns. 3 and 4, the deflection estimates utilize ratios of measured period between reference events T₁through T₄and the period of forced oscillations P. Provided that all of these time intervals are obtained using the same reference clock, the final deflection (and, therefore, force) estimate advantageously becomes insensitive to clock systematic errors, such as, for example, drift due to aging, temperature, or other environmental changes. The calculation method of Eqns. 3 and 4 is also insensitive to changes in resonant frequency with temperature or other environmental effects.

In another embodiment of the invention, a clock jitter or variation (e.g., on the order of no more than a half clock cycle in one implementation) is purposely introduced into the reference clock such that low frequency inertial forces applied to the sensor can be averaged over time. As is well known, quantization noise or error cannot be averaged; introduction of such jitter advantageously mitigates or eliminates such quantization error, thereby allowing for effective averaging (and hence increasing the accuracy of the device).

<figref idref="DRAWINGS">FIG. 8A</figref> is a plot of the oscillation amplitude of the tuning fork <b>14</b> with respect to the frame <b>12</b> showing the three triggering points <b>56</b>, <b>58</b>, and <b>60</b>, described above. <figref idref="DRAWINGS">FIG. 8B</figref> is, in part, a pictorial representation of the triggering events <b>56</b>, <b>58</b>, and <b>60</b>. At trigger event <b>58</b> a tunneling discharge pulse <b>100</b> tunnels from the tuning fork <b>14</b> to the frame <b>12</b>. At trigger event <b>56</b>, two tunneling discharge pulses <b>102</b> and <b>103</b> tunnel from the tuning fork <b>14</b> to the frame <b>12</b>. At trigger event <b>60</b>, a tunneling discharge pulse <b>104</b> tunnels from the tuning fork <b>14</b> to the frame <b>12</b>. As the pulses <b>100</b>, <b>102</b>, <b>103</b>, and <b>104</b> may differ in amplitude due to, for example, variations in applied tunneling voltage (voltage noise) and/or tunneling distance, low noise current amplifiers may be used to amplify the discharge pulses to the rail (that is the maximum current level value of the sensing circuit) so as to produce the amplified pulses <b>106</b>, <b>108</b>, <b>109</b>, and <b>110</b> respectively, which exhibit substantially rectangular shapes, as shown in <figref idref="DRAWINGS">FIG. 8B</figref>. Although the amplitude information is lost, the amplified square pulses <b>106</b>, <b>108</b>, <b>109</b>, and <b>110</b> are advantageously well suited for interfacing with digital circuits.

The tuning fork gyroscope <b>10</b> provides a compact, mechanically-isolated design to measure the Coriolis force caused by rotation of the gyroscope <b>10</b>. Rotation along the length of the first and second prongs <b>24</b> and <b>26</b> will cause a Coriolis force raising or lowering the prongs out of the original plane (e.g., the x-y plane shown in <figref idref="DRAWINGS">FIG. 1</figref>) 90° out of phase with the prong vibration. If the resonant frequency of a given prong vibrating in and out of the plane is matched to the resonant frequency of the prong vibrating in the plane, then the amplitude of the vertical vibration should be proportional to the total angle rotated. If the two orthogonal vibrations are significantly off resonance from each other, then the vertical offset of the prong will be proportional to the change in rotation times the horizontal prong velocity.

<figref idref="DRAWINGS">FIG. 9</figref> is a top view of an embodiment of the gyroscope <b>10</b> wherein the digital position triggers <b>20</b> are located on the free ends of the first and second prongs <b>24</b> and <b>26</b>. In this embodiment, an edge <b>112</b> of the conductive plane <b>34</b> is curved such that as the prongs oscillate in the x-direction the size of the gap <b>42</b> remains substantially the same.

<figref idref="DRAWINGS">FIG. 10</figref> is a side cross-section side view of an embodiment of the gyroscope <b>10</b> further comprising a third driver <b>114</b> configured to drive the tuning fork <b>14</b> to oscillate with respect to the frame <b>12</b> in the z-direction. This embodiment of the gyroscope <b>10</b> also comprises a capping wafer <b>116</b>, an integral frame/base wafer assembly <b>118</b>, and a bonding layer <b>120</b>.

<figref idref="DRAWINGS">FIG. 11</figref> is a plot of the displacement of the conductive tips <b>32</b> in the z-direction over time with respect to the conductive plane <b>34</b> of one of the digital triggers <b>20</b> depicted in <figref idref="DRAWINGS">FIGS. 2A-2B</figref>. In <figref idref="DRAWINGS">FIG. 11</figref>, the x- and z-direction resonances of the prong to which the digital trigger <b>20</b> is coupled are matched. If the z-direction resonant frequency of a given prong matches its x-direction resonant frequency, the Coriolis force due to rotation of the frame <b>12</b> about the y-axis will couple into the resonant oscillation and will be expressed as a change in amplitude of the z-direction oscillation of the given prong. The long-dashed line corresponds to pre-existing oscillation of the given prong in the z-direction with respect to the frame <b>12</b>. The solid line corresponds to the x-direction displacement of the given prong with respect to the frame <b>12</b>. The dotted line represents the total displacement of the given prong in the z-direction with respect to the frame <b>12</b>. The dot-dash-dot line corresponds to the displacement of the given prong in the z-direction with respect to the frame <b>12</b> attributable to the Coriolis force.

<figref idref="DRAWINGS">FIG. 12</figref> is a plot of the z-direction-displacement of the conductive tips <b>32</b> with respect to the conductive plane <b>34</b> of one of the digital triggers <b>20</b> depicted in <figref idref="DRAWINGS">FIGS. 2A-2B</figref> against the x-direction-displacement of the conductive tips <b>32</b> with respect to the conductive plane <b>34</b>. In <figref idref="DRAWINGS">FIG. 12</figref>, the x- and z-direction resonances of the prong, to which the digital trigger <b>20</b> is coupled, are matched. The solid line in <figref idref="DRAWINGS">FIG. 12</figref> corresponds to the total displacement of the given prong with respect to the frame <b>12</b>. The dashed line in <figref idref="DRAWINGS">FIG. 12</figref> corresponds to the displacement of the given prong with respect to the frame <b>12</b> attributable to the Coriolis force.

<figref idref="DRAWINGS">FIG. 13</figref>, like <figref idref="DRAWINGS">FIG. 11</figref>, is a plot of the z-direction-displacement over time of the conductive tips <b>32</b> with respect to the conductive plane <b>34</b> of one of the digital triggers <b>20</b> depicted in <figref idref="DRAWINGS">FIGS. 2A-2B</figref>. However, <figref idref="DRAWINGS">FIG. 13</figref> differs from <figref idref="DRAWINGS">FIG. 11</figref> in that in <figref idref="DRAWINGS">FIG. 13</figref>, the x- and z-direction resonances of the prong to which the digital trigger <b>20</b> is coupled are mis-matched, but instead, the z-direction resonant frequency of the prong is much greater than that of the x-direction resonant frequency. In this scenario, the Coriolis force may be determined by calculating the z-direction offset of a previously initiated resonant z-direction oscillation. The initial vertical and horizontal resonant oscillation of the prong may be induced by using capacitive forcing to an initial vertical and horizontal displacement. Besides capacitive forcing, the initial resonant z-direction oscillation may also be caused by a resonant tone generator, or any other forcing means. By averaging the results from the two prongs (vibrating in the x-direction 180° out of phase) non-rotational acceleration effects can be eliminated from the measurement. The solid line in <figref idref="DRAWINGS">FIG. 13</figref> corresponds to pre-existing oscillation of the given prong in the z-direction with respect to the frame <b>12</b>. The dash-dot-dash line in <figref idref="DRAWINGS">FIG. 13</figref> corresponds to the x-direction displacement of the given prong with respect to the frame <b>12</b>. The dotted line in <figref idref="DRAWINGS">FIG. 13</figref> represents the total displacement of the given prong in the z-direction with respect to the frame <b>12</b>. The dashed line in <figref idref="DRAWINGS">FIG. 13</figref> corresponds to the displacement of the given prong in the z-direction with respect to the frame <b>12</b> attributable to the Coriolis force.

<figref idref="DRAWINGS">FIG. 14</figref> is a plot of the z-direction-displacement of the conductive tips <b>32</b> with respect to the conductive plane <b>34</b> of one of the digital triggers <b>20</b> depicted in <figref idref="DRAWINGS">FIGS. 2A-2B</figref> against the x-direction-displacement of the conductive tips <b>32</b> with respect to the conductive plane <b>34</b> where the x- and z-direction resonances of the prong, to which the digital trigger <b>20</b> is coupled, are mis-matched. The solid line in <figref idref="DRAWINGS">FIG. 14</figref> corresponds to the total displacement of the given prong with respect to the frame <b>12</b>. The dashed line in <figref idref="DRAWINGS">FIG. 14</figref> corresponds to the displacement of the given prong with respect to the frame <b>12</b> attributable to the Coriolis force.

<figref idref="DRAWINGS">FIGS. 15A-15B</figref> are perspective views of an embodiment of the gyroscope <b>10</b>. In this embodiment, the digital position triggers <b>20</b> are located on opposite sides of the distal end <b>30</b> of the base <b>22</b>. Although four digital triggers <b>20</b> are depicted in <figref idref="DRAWINGS">FIGS. 15A-15B</figref>, it is to be understood that any number of at least two digital switches <b>20</b> may be used with the gyroscope <b>10</b>, and that the four digital triggers <b>20</b> merely represent one example embodiment. In this embodiment, when a torque, due to Coriolis forces <b>122</b>, is applied to the tuning fork <b>14</b>, the base twists causing relative motion between the distal end <b>30</b> of the base <b>22</b> and the frame <b>12</b> (not shown in <figref idref="DRAWINGS">FIGS. 15A-15B</figref>) such that the Coriolis forces acting on both prongs may be combined into one time domain measurement. In this embodiment, half of each digital trigger <b>20</b> may be mounted to the distal end <b>30</b> of the base <b>22</b>, as shown in <figref idref="DRAWINGS">FIGS. 15A-15B</figref> while the corresponding half of each digital trigger <b>20</b> may be mounted to the frame <b>12</b> (not shown). Each half of the digital trigger <b>20</b> may comprise a z-direction-stacked set of electron tunneling tips. <figref idref="DRAWINGS">FIG. 15B</figref> illustrates how the shape of the base <b>22</b> may be altered in order to tune the rotational resonant frequency of the tuning fork <b>14</b> to match, or mismatch, the Coriolis force depending on the desired mode of operation.

<figref idref="DRAWINGS">FIG. 16</figref> is a perspective view of an embodiment of the gyroscope <b>10</b> wherein the tuning fork <b>14</b> further comprises first and second arms <b>124</b> and <b>126</b> respectively having proximal and distal ends <b>128</b> and <b>130</b> respectively. The proximal ends <b>128</b> of the first and second arms <b>124</b> and <b>126</b> are coupled to the distal end of the base <b>30</b>. The position triggers <b>20</b> are located on the distal ends <b>130</b> of the first and second arms <b>124</b> and <b>126</b>. The first and second prongs <b>24</b> and <b>26</b> are subjected to oscillating driving forces <b>132</b> such that the first and second prongs <b>24</b> and <b>26</b> oscillate at their resonant frequencies 180° out of phase with each other. When the gyroscope <b>10</b> is subjected to a rotation about the y-axis, Coriolis forces <b>122</b> cause deflection of the first and second prongs, which in turn causes the tuning fork <b>14</b> to twist. The twisting of the tuning fork <b>14</b> causes displacement of the distal ends <b>130</b> of the first and second arms <b>124</b> and <b>126</b>, which can be measured by the digital triggers <b>20</b>.

<figref idref="DRAWINGS">FIG. 17</figref> is a perspective view of an embodiment of the gyroscope <b>10</b> wherein the tuning fork <b>14</b> further comprises third and fourth arms <b>134</b> and <b>136</b>. <figref idref="DRAWINGS">FIG. 17</figref> also illustrates an alternate orientation of the digital triggers <b>20</b>.

From the above description of the gyroscope <b>10</b>, it is manifest that various techniques may be used for implementing the concepts of gyroscope <b>10</b> without departing from its scope. The described embodiments are to be considered in all respects as illustrative and not restrictive. It should also be understood that gyroscope <b>10</b> is not limited to the particular embodiments described herein, but is capable of many embodiments without departing from the scope of the claims.